Free vibration of axially loaded composite beams with general boundary conditions using hyperbolic shear deformation theory

Composite Structures

Volumn 97, Issue , 2013, Pages 1-14

  Li, Jun ^a   Shi, Chaoxing ^a   Kong, Xiangshao ^a   Li, Xiaobin ^a   Wu, Weiguo ^a  

^a WUHAN UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Axial force; Buckling; Free vibration; Hyperbolic shear deformation; Laminated beam; Poisson effect

Indexed keywords

AXIAL FORCES; BUCKLING BEHAVIORS; BUCKLING LOADS; COMPOSITE BEAM; FREE VIBRATION; GENERAL BOUNDARY CONDITIONS; GOVERNING DIFFERENTIAL EQUATIONS; ILLUSTRATIVE EXAMPLES; LAMINATED BEAMS; LAMINATED COMPOSITE BEAM; MODE SHAPES; POISSON EFFECTS; ROTARY INERTIAS; SHEAR DEFORMATION THEORY; SPECTRAL ELEMENT; SPECTRAL FINITE ELEMENT METHOD; TRANSVERSE DEFORMATION; WITTRICK WILLIAMS ALGORITHMS;

AXIAL FLOW; BUCKLING; COMPOSITE BEAMS AND GIRDERS; LAMINATED COMPOSITES; SHEAR DEFORMATION;

BOUNDARY CONDITIONS;

EID: 84871479097     PISSN: 02638223     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compstruct.2012.10.014     Document Type: Article

References (59)

1. Abarcar R.B., Cunniff P.F. The vibration of cantilever beams of fiber reinforced material. J Compos Mater 1972, 6:504-517.
2. Miller A.K., Adams D.F. An analytic means of determining the flexural and torsional resonant frequencies of generally orthotropic beams. J Sound Vib 1975, 41:433-449.
3. Vinson J.R., Sierakowski R.L. The behavior of structures composed of composite materials 2004, Kluwer, New York. 2nd ed.
4. Banerjee J.R., Williams F.W. Free vibration of composite beams - an exact method using symbolic computation. J Aircraft 1995, 32:636-642.
5. Mahapatra D.R., Gopalakrishnan S., Sankar T.S. Spectral-element-based solutions for wave propagation analysis of multiply connected unsymmetric laminated composite beams. J Sound Vib 2000, 237:819-836.
6. Teoh L.S., Huang C.C. The vibration of beams of fibre reinforced material. J Sound Vib 1977, 51:467-473.
7. Teh K.K., Huang C.C. The vibrations of generally orthotropic beams, a finite element approach. J Sound Vib 1979, 62:195-206.
8. Chen A.T., Yang T.Y. Static and dynamic formulation of symmetrically laminated beam finite element for microcomputer. J Compos Mater 1985, 19:459-475.
9. Chandrashekhara K., Krishnamurthy K., Roy S. Free vibration of composite beams including rotary inertia and shear deformation. Compos Struct 1990, 14:269-279.
10. Abramovich H. Shear deformation and rotatory inertia effects of vibrating composite beams. Compos Struct 1992, 20:165-173.
11. Krishnaswamy S., Chandrashekhara K., Wu W.Z.B. Analytical solutions to vibration of generally layered composite beams. J Sound Vib 1992, 159:85-99.
12. Abramovich H., Livshits A. Free vibration of non-symmetric cross-ply laminated composite beams. J Sound Vib 1994, 176:597-612.
13. Nabi S.M., Ganesan N. A generalized element for the free vibration analysis of composite beam. Comput Struct 1994, 51:607-610.
14. Eisenberger M., Abramovich H., Shulepov O. Dynamic stiffness analysis of laminated beams using first order shear deformation theory. Compos Struct 1995, 31:265-271.
15. Teboub Y., Hajela P. Free vibration of generally layered composite beams using symbolic computations. Compos Struct 1995, 33:123-134.
16. Abramovich H., Eisenberger M., Shulepov O. Vibrations and buckling of cross-ply nonsymmetric laminated composite beams. AIAA J 1996, 34:1064-1069.
17. Banerjee J.R. Free vibration of axially loaded composite Timoshenko beams using the dynamic stiffness matrix method. Comput Struct 1998, 69:197-208.
18. Yildirim V., Sancaktar E., Kiral E. Comparison of the in-plane natural frequencies of symmetric cross-ply laminated beams based on the Bernoulli-Euler and Timoshenko beam theories. J Appl Mech - Trans ASME 1999, 66:410-417.
19. Yildirim V. Effect of the longitudinal to transverse moduli ratio on the in-plane natural frequencies of symmetric cross-ply laminated beams by the stiffness method. Compos Struct 2000, 50:319-326.
20. Chakraborty A., Mahapatra D.R., Gopalakrishnan S. Finite element analysis of free vibration and wave propagation in asymmetric composite beams with structural discontinuities. Compos Struct 2002, 55:23-36.
21. Mahapatra D.R., Gopalakrishnan S. A spectral finite element model for analysis of axial-flexural-shear coupled wave propagation in laminated composite beams. Compos Struct 2003, 59:67-88.
22. Ruotolo R. A spectral element for laminated composite beams: theory and application to pyroshock analysis. J Sound Vib 2004, 270:149-169.
23. Goyal V.K., Kapania R.K. A shear-deformable beam element for the analysis of laminated composites. Finite Elem Anal Des 2007, 43:463-477.
24. Banerjee J.R., Cheung C.W., Morishima R., Perera M., Njuguna J. Free vibration of a three-layered sandwich beam using the dynamic stiffness method and experiment. Int J Solids Struct 2007, 44:7543-7563.
25. Carrera E., Giunta G. Refined beam theories based on a unified formulation. Int J Appl Mech 2010, 2:117-143.
26. Carrera E., Giunta G., Nali P., Petrolo M. Refined beam elements with arbitrary cross-section geometries. Comput Struct 2010, 88:283-293.
27. Bhimaraddi A., Chandrashekhara K. Some observations on the modeling of laminated composite beams with general lay-ups. Compos Struct 1991, 19:371-380.
28. Soldatos K.P., Elishakoff I. A transverse shear and normal deformable orthotropic beam theory. J Sound Vib 1992, 154:528-533.
29. Chandrashekhara K., Bangera K.M. Free vibration of composite beams using a refined shear flexible beam element. Comput Struct 1992, 43:719-727.
30. Khdeir A.A., Reddy J.N. Free vibration of cross-ply laminated beams with arbitrary boundary conditions. Int J Eng Sci 1994, 32:1971-1980.
31. Marur S.R., Kant T. Free vibration analysis of fiber reinforced composite beams using higher order theories and finite element modelling. J Sound Vib 1996, 194:337-351.
32. Song S.J., Waas A.M. Effects of shear deformation on buckling and free vibration of laminated composite beams. Compos Struct 1997, 37:33-43.
33. Kant T., Marur S.R., Rao G.S. Analytical solution to the dynamic analysis of laminated beams using higher order refined theory. Compos Struct 1998, 40:1-9.
34. Khdeir A.A., Reddy J.N. Buckling of cross-ply laminated beams with arbitrary boundary conditions. Compos Struct 1997, 37:1-3.
35. Karama M., Abou Harb B., Mistou S., Caperaa S. Bending, buckling and free vibration of laminated composite with a transverse shear stress continuity model. Compos Part B - Eng 1998, 29:223-234.
36. Shi G., Lam K.Y. Finite element vibration analysis of composite beams based on higher-order beam theory. J Sound Vib 1999, 219:707-721.
37. Rao M.K., Desai Y.M., Chitnis M.R. Free vibrations of laminated beams using mixed theory. Compos Struct 2001, 52:149-160.
38. Ghugal Y M., Shimpi R.P. A review of refined shear deformation theories for isotropic and anisotropic laminated beams. J Reinf Plast Compos 2001, 20:255-272.
39. Matsunaga H. Vibration and buckling of multilayered composite beams according to higher order deformation theories. J Sound Vib 2001, 246:47-62.
40. Shimpi R.P., Ainapure A.V. Free vibration analysis of two layered cross-ply laminated beams using layer-wise trigonometric shear deformation theory. J Reinf Plast Compos 2002, 21:1477-1492.
41. Chen W.Q., Lv C.F., Bian Z.G. Elasticity solution for free vibration of laminated beams. Compos Struct 2003, 62:75-82.
42. Karama M., Afaq K.S., Mistou S. Mechanical behaviour of laminated composite beam by the new multi-layered laminated composite structures model with transverse shear stress continuity. Int J Solids Struct 2003, 40:1525-1546.
43. Chen W.Q., Lv C.F., Bian Z.G. Free vibration analysis of generally laminated beams via state-space-based differential quadrature. Compos Struct 2004, 63:417-425.
44. Kapuria S., Dumir P.C., Jain N.K. Assessment of zigzag theory for static loading, buckling, free and forced response of composite and sandwich beams. Compos Struct 2004, 64:317-327.
45. Murthy M.V.V.S., Mahapatra D.R., Badarinarayana K., Gopalakrishnan S. A refined higher order finite element for asymmetric composite beams. Compos Struct 2005, 67:27-35.
46. Aydogdu M. Vibration analysis of cross-ply laminated beams with general boundary conditions by Ritz method. Int J Mech Sci 2005, 47:1740-1755.
47. Aydogdu M. Buckling analysis of cross-ply laminated beams with general boundary conditions by Ritz method. Compos Sci Technol 2006, 66:1248-1255.
48. Aydogdu M. Free vibration analysis of angle-ply laminated beams with general boundary conditions. J Reinf Plast Compos 2006, 25:1571-1583.
49. Subramanian P. Dynamic analysis of laminated composite beams using higher order theories and finite elements. Compos Struct 2006, 73:342-353.
50. Aydogdu M. Thermal buckling analysis of cross-ply laminated composite beams with general boundary conditions. Compos Sci Technol 2007, 67:1096-1104.
51. Marur S.R., Kant T. On the angle ply higher order beam vibrations. Comput Mech 2007, 40:25-33.
52. Vidal P., Polit O. A family of sinus finite elements for the analysis of rectangular laminated beams. Compos Struct 2008, 84:56-72.
53. Vidal P., Polit O. Vibration of multilayered beams using sinus finite elements with transverse normal stress. Compos Struct 2010, 92:1524-1534.
54. Vidal P., Polit O. A sine finite element using a zig-zag function for the analysis of laminated composite beams. Compos Part B - Eng 2011, 42:1671-1682.
55. Soldatos K.P. A transverse shear deformation theory for homogeneous monoclinic plates. Acta Mech 1992, 94:195-220.
56. Lee U. Spectral element method in structural dynamics 2004, Inha University Press, Incheon (Korea).
57. Gopalakrishnan S., Chakraborty A., Roy Mahapatra D. Spectral finite element method 2007, Springer-Verlag, London.
58. Jones R.M. Mechanics of composite materials 1976, McGraw-Hill, New York.
59. Wittrick W.H., Williams F.W. A general algorithm for computing natural frequencies of elastic structures. Quart. J Mech Appl Math 1971, 24:263-284.